# Descriptive Kernel Convolution Network with Improved Random Walk Kernel

arXiv: https://arxiv.org/abs/2402.06087 · HTML: https://mlsanity.com/paper/2402.06087/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 63 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 30 of 39)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [A Survey on The Expressive Power of Graph Neural Networks](https://mlsanity.com/paper/2003.04078/) (2020)
- [KerGNNs: Interpretable Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/2201.00491/) (2022)
- [Convolutional Kernel Networks](https://mlsanity.com/paper/1406.3332/) (2014)
- [On Evaluation Metrics for Graph Generative Models](https://mlsanity.com/paper/2201.09871/) (2022)
- [Graph Kernels: A Survey](https://mlsanity.com/paper/1904.12218/) (2019)
- [TwiBot-22: Towards Graph-Based Twitter Bot Detection](https://mlsanity.com/paper/2206.04564/) (2022)
- [Convolutional Kernel Networks for Graph-Structured Data](https://mlsanity.com/paper/2003.05189/) (2020)
- [RetGK: Graph Kernels based on Return Probabilities of Random Walks](https://mlsanity.com/paper/1809.02670/) (2018)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [Steps Toward Deep Kernel Methods from Infinite Neural Networks](https://mlsanity.com/paper/1508.05133/) (2015)
- [End-to-End Kernel Learning with Supervised Convolutional Kernel Networks](https://mlsanity.com/paper/1605.06265/) (2016)

## Built on by (most cited first, 5 of 5)

- [On the Detection of Reviewer-Author Collusion Rings From Paper Bidding](https://mlsanity.com/paper/2402.07860/) (2024)
- [MoSE: Unveiling Structural Patterns in Graphs via Mixture of Subgraph Experts](https://mlsanity.com/paper/2509.09337/) (2025)
- [Exploring Consistency in Graph Representations:from Graph Kernels to Graph Neural Networks](https://mlsanity.com/paper/2410.23748/) (2024)
- [Disentangled Graph Representation Based on Substructure-Aware Graph Optimal Matching Kernel Convolutional Networks](https://mlsanity.com/paper/2504.16360/) (2025)
- [FRAUDGUESS: Spotting and Explaining New Types of Fraud in Million-Scale Financial Data](https://mlsanity.com/paper/2509.15493/) (2025)

## Abstract (arXiv)

Graph kernels used to be the dominant approach to feature engineering for structured data, which are superseded by modern GNNs as the former lacks learnability. Recently, a suite of Kernel Convolution Networks (KCNs) successfully revitalized graph kernels by introducing learnability, which convolves input with learnable hidden graphs using a certain graph kernel. The random walk kernel (RWK) has been used as the default kernel in many KCNs, gaining increasing attention. In this paper, we first revisit the RWK and its current usage in KCNs, revealing several shortcomings of the existing designs, and propose an improved graph kernel RWK+, by introducing color-matching random walks and deriving its efficient computation. We then propose RWK+CN, a KCN that uses RWK+ as the core kernel to learn descriptive graph features with an unsupervised objective, which can not be achieved by GNNs. Further, by unrolling RWK+, we discover its connection with a regular GCN layer, and propose a novel GNN layer RWK+Conv. In the first part of experiments, we demonstrate the descriptive learning ability of RWK+CN with the improved random walk kernel RWK+ on unsupervised pattern mining tasks; in the second part, we show the effectiveness of RWK+ for a variety of KCN architectures and supervised graph learning tasks, and demonstrate the expressiveness of RWK+Conv layer, especially on the graph-level tasks. RWK+ and RWK+Conv adapt to various real-world applications, including web applications such as bot detection in a web-scale Twitter social network, and community classification in Reddit social interaction networks.